Root neighborhoods of a polynomial
Mathematics of Computation
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Efficient algorithms for computing the nearest polynomial with constrained roots
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Efficient algorithms for computing the nearest polynomial with a real root and related problems
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
The nearest polynomial with a given zero, and similar problems
ACM SIGSAM Bulletin
Robust Control: The Parametric Approach
Robust Control: The Parametric Approach
A note on a nearest polynomial with a given root
ACM SIGSAM Bulletin
The nearest polynomial with a given zero, revisited
ACM SIGSAM Bulletin
Locating real multiple zeros of a real interval polynomial
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
The nearest polynomial with a zero in a given domain from a geometrical viewpoint
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Real Algebraic Numbers: Complexity Analysis and Experimentation
Reliable Implementation of Real Number Algorithms: Theory and Practice
The nearest polynomial with a zero in a given domain
Theoretical Computer Science
On the asymptotic and practical complexity of solving bivariate systems over the reals
Journal of Symbolic Computation
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For a real univariate polynomial f and a closed complex domain D whose boundary C is a simple curve parameterized by a univariate piecewise rational function, a rigorous method is given for finding a real univariate polynomial f@? such that f@? has a zero in D and @?f-f@?@?"~ is minimal. First, it is proved that the minimum distance between f and polynomials having a zero at @a@?C is a piecewise rational function of the real and imaginary parts of @a. Thus, on C, the minimum distance is a piecewise rational function of a parameter obtained through the parameterization of C. Therefore, f@? can be constructed by using the property that f@? has a zero on C and computing the minimum distance on C. We analyze the asymptotic bit complexity of the method and show that it is of polynomial order in the size of the input.